Closed-Form Bounds for DP-SGD against Record-level Inference
- Giovanni Cherubin ,
- Boris Köpf ,
- Andrew Paverd ,
- Shruti Tople ,
- Lukas Wutschitz ,
- Santiago Zanella-Béguelin
Published by USENIX Association
![Bayes Security (β*, higher better) of DP-SGD against membership and attribute inference on the Adult and Purchase datasets as a function of the number of training steps. The green dashed line shows the corresponding DP budget (ε). Membership and attribute inference curves decrease monotonically as the model is trained for longer and the accuracy and DP budget grow.](https://cdn.statically.io/img/www.microsoft.com/en-us/research/uploads/prodnew/2024/04/accuracy-privacy.png)
Machine learning models trained with differentially-private (DP) algorithms such as DP-SGD enjoy resilience against a wide range of privacy attacks. Although it is possible to derive bounds for some attacks based solely on an (ε,δ)-DP guarantee, meaningful bounds require a small enough privacy budget (i.e., injecting a large amount of noise), which results in a large loss in utility. This paper presents a new approach to evaluate the privacy of machine learning models against specific record-level threats, such as membership and attribute inference, without the indirection through DP. We focus on the popular DP-SGD algorithm, and derive simple closed-form bounds. Our proofs model DP-SGD as an information theoretic channel whose inputs are the secrets that an attacker wants to infer (e.g., membership of a data record) and whose outputs are the intermediate model parameters produced by iterative optimization. We obtain bounds for membership inference that match state-of-the-art techniques, whilst being orders of magnitude faster to compute. Additionally, we present a novel data-dependent bound against attribute inference. Our results provide a direct, interpretable, and practical way to evaluate the privacy of trained models against specific inference threats without sacrificing utility.